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**A hybrid gradient-projection algorithm for averaged mappings in Hilbert spaces.**
*(English)*
Zbl 1252.49013

Summary: It is well known that the Gradient-Projection Algorithm (GPA) is very useful in solving constrained convex minimization problems. In this paper, we combine a general iterative method with the gradient-projection algorithm to propose a hybrid gradient-projection algorithm and prove that the sequence generated by the hybrid gradient-projection algorithm converges in norm to a minimizer of constrained convex minimization problems which solves a variational inequality.

### MSC:

49J40 | Variational inequalities |

47J25 | Iterative procedures involving nonlinear operators |

49J45 | Methods involving semicontinuity and convergence; relaxation |

90C30 | Nonlinear programming |

74B99 | Elastic materials |

### Keywords:

gradient-projection algorithm; averaged mappings in Hilbert spaces; constrained convex minimization problems; variational inequality
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\textit{M. Tian} and \textit{M.-M. Li}, J. Appl. Math. 2012, Article ID 782960, 14 p. (2012; Zbl 1252.49013)

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### References:

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